Ms Gillard has ruled out changes to Labour's proposed mining tax, which could have been an important bargaining chip during discussions to win support from key independents.
Neither Labour nor the coalition secured the 76 seats needed to govern in their own right following Saturday's election.
Ms Gillard and Opposition Leader Tony Abbott flew into Canberra on Monday and are due to begin negotiations with a trio of independents who are tipped to hold the key to government.
Rob Oakeshott, Tony Windsor and Bob Katter are due to arrive in the national capital over the next 24 hours.
They're expected to have their own discussions, as well as talks with both leaders.
Ms Gillard told reporters she wasn't prepared to discuss publicly what she was willing to do to gain support for her government.
"I'm not going to play games of ruling things in and ruling things out," she said.
But she vowed transparency once a deal was negotiated.
Mr Abbott was keeping a low profile, while Labour insisted it had the mandate to govern because it had won the popular vote.
Three other important players in these uncertain times are Andrew Wilkie, an independent who may still win the seat of Denison from Labour, the Australian Greens' Adam Bandt, who snatched Melbourne from the government, and WA Nationals giant-slayer Tony Crook, who ousted Liberal veteran Wilson Tuckey.
Mr Bandt has signalled he's more inclined to work with Labour, while Mr Wilkie would be willing to talk to both Labour and the coalition.
While Mr Crook comes from the conservative side of politics, he has indicated he is considering sitting on the crossbenches and would entertain working with Labour - if it abandoned the mining tax.
But Ms Gillard insisted the tax was here to stay.
"Obviously I entered breakthrough negotiations with the Australian miners, Australia's biggest miners, and I will be honouring that agreement," she told reporters in Canberra.
Mr Crook later declared that was a "major stumbling block" to him supporting a minority Labour government.
"We wanted no mining tax," he said.
"To that end it's very likely we're not going to be talking to Ms Gillard."
The 2010 election has cemented its place in the history books by delivering the first hung parliament since 1940.
But the situation became even more unusual when Governor-General Quentin Bryce confirmed she was seeking advice relating to concerns about her family connection to Labour powerbroker Bill Shorten, who is married to her daughter Chloe.
Labour will need to show the governor-general it can command a majority on the floor of parliament's lower house to win her approval for minority government.
In a statement posted on the governor-general's website, her office said: "The governor-general is seeking advice on concerns raised about her personal position in the current political circumstances."
There were frustrations on both sides of politics following the election outcome, which remains far from clear.
On Monday afternoon, the count stood at three seats to independents, 72 for Labour, the coalition had 70 - taking into account Mr Crook in O'Connor - and the Greens had one.
Four remain in doubt - Boothby, Denison, Hasluck and Dunkley.
In Perth, former state government minister Alannah MacTiernan, who tried to take the seat of Canning from Liberal Don Randall, voiced concerns about the Labour campaign.
"After having been in government, you can't just rely on saying `the reason you should vote for us is the other bloke is really bad'," she told ABC radio.
"You've got to have a strong message ... and sell your positives.
"Another big mistake that was made over was a refusal to deal with the issue of the mining tax."
But the fallout wasn't confined to Labour.
High-profile Tasmanian backbencher Guy Barnett, who looks likely to lose his Senate position, took aim at fellow senator Eric Abetz, a senior conservative powerbroker.
"I think there should be a wholesale review. Senator Abetz is clearly a very influential powerbroker, and he has to stand responsible for his decisions and his actions, as do others in leadership in the party," he said.
